My armature deformations inexplicably 'pop', without any shape keys or other modifiers. What's going on?
When in doubt, check out the various settings in Properties >> Bone Settings >> Deform Tab.  If there's more than one segment under 'Curved Bones', try dialing it down to 1.  While sub-dividing curved bones can lead to higher-resolution deformations, they are also problematic, and hard to trouble-shoot.  If you really want to have those high-resolution deformations, try selecting 'Multiply' on the deformation settings for nearby, connected bones.  Also do lots of testing before animating.